Respuesta final al problema
$x^{2}-x+1+\frac{-1}{1+x}$
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Solución explicada paso por paso
1
Realizamos la división de polinomios, $x^3$ entre $1+x$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}+1;}{\phantom{;}x^{2}-x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}+1\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}+1;}\underline{-x^{3}-x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{3}-x^{2};}-x^{2}\phantom{-;x^n}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n;}\underline{\phantom{;}x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{;\phantom{;}x^{2}+x\phantom{;}-;x^n;}\phantom{;}x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}+1-;x^n-;x^n;}\underline{-x\phantom{;}-1\phantom{;}\phantom{;}}\\\phantom{;;-x\phantom{;}-1\phantom{;}\phantom{;}-;x^n-;x^n;}-1\phantom{;}\phantom{;}\\\end{array}$
2
Polinomio resultado de la división
$x^{2}-x+1+\frac{-1}{1+x}$
Respuesta final al problema
$x^{2}-x+1+\frac{-1}{1+x}$